A better approach is to use more of the points near the peak to improveaccuracy. A technique that applies this idea to transmission (S21)measurements of the Q of a cavityis described admirablybyLeong andMazierska [5]. Their method involves fitting a circle to complex S21values plotted on a Smith Chart, and removes the effects of cables, connectors,and mismatches to give an accurate determination of Q-factorsin the range 103–107. It is well-suited to precision metrology, in a setupwhere phase information is available.

The Handbook of Filter Systhesis written in 1967 stands unchallenged as THE definitive reference; highpass, bandpass, lowpass and bandstop (notch). Chebychev, Gaussian, Bessel, Linear Phase, Elliptical functions; its all there. If Zverev were alive today, he would no doubt vigorously challenge 5 digit Qs, as I think we all should in non-optical systems.

I cannot refute any claim, as I did not witness the test procedure...its simply a red flag based on my personal experience.

In other words (please correct me if I'm wrong) in all your extensive professional experience you are not aware of IEEE or other organization's standard method for measuring and reporting loaded Q's. If that is correct, then this controversy could simply be a case of different researchers reporting Q measurements based on different standards.

Q is definitely in the eye of the beholder. In the world, its simply ctr/3db BW. Not all systems are bandpass, so other definitions are created. This paper from Brookhaven National Labs is an example where S21 is less straight forward since they have an unusual cavity type:

"This paper discussed the conventional -3dB method of Q values measurement in the room temperature cavity and the issues of this method caused bythe field polarization of the slightlty elliptical cavity. The reasons of cavity polarization, which causes the S21 distortion, were described. The new S21 formula for the splitting modes was derived and used to fit the measurement data. The fitted S21 and Q values match the simulated results very well."

As resonant cavity, like a frustum, is inherently Bandpass and should have a center frequency and 3db (half power) bandwidth. Those claiming 1.1:1 VSWR and a Q of over 20K might have just invented the world's best BP filter. I seriously doubt the robust commercial filter suppliers would have not known about this for decades.

So my professional guess is one of 3 things:

1) They aren't filter people and applied other calculations which inflated Q in comparison to typical industry standards.2) They purposely defined Q high nefariously.3) A combination of above.

Waskly Wabbit, you...very obvious you're thinking. I've skirted this also, but not as thoroughly. If this were true, why the different end plate diameters? These bad boys should also show force, but to my knowledge never have: http://www.eham.net/data/classifieds/images/332154.jpg

Hm... true, this should be true for cylindrical cavities too, provided the RF feed is injected at an asymmetric point in the cavity, but nobody has seen that. Hm.

Maybe I'm oversimplifying the problem... just considering the power hitting the plates might not be enough, in theory we'd have to analyse the evolution of the (delayed) power distribution on the whole body of the frustum over the modulation time, and solve Maxwell's equations properly. A bit like what Greg Egan did with the standing waves, but also considering an LFO modulation of the power (is that possible?).

(I think somebody has already pointed out on this thread that Egan's solution, although correct for a resonant EM field with no change in power, was not taking into account the continuous RF feed from the antenna in equilibrium with heat dissipation, equilibrium that I think is transiently broken by input power modulation... but I may be wrong)

My maths is not good enough to do the proper analysis. Intuitively, it would seem to me that there should be an LFO of the EM field in the frustum. But then why wouldn't it be there for a cylinder too?

On the other hand, the net effect integrated over an integer number of periods is still zero. Maybe really nobody noticed.

A better approach is to use more of the points near the peak to improveaccuracy. A technique that applies this idea to transmission (S21)measurements of the Q of a cavityis described admirablybyLeong andMazierska [5]. Their method involves fitting a circle to complex S21values plotted on a Smith Chart, and removes the effects of cables, connectors,and mismatches to give an accurate determination of Q-factorsin the range 103–107. It is well-suited to precision metrology, in a setupwhere phase information is available.

It is exactly that. The mass at any time after you start the engine is (m - Ein/c^2). It is the mass you started with minus the mass you are using to accelerate. In your derivation, you hand wave this part by saying Ein, when in fact, there is no input to the system. Then you ignore where the energy is coming from by assuming that what comes out of the battery has negligible mass, then claim over unity by counting the energy gained from that expenditure as gravy.

Paradox resolved, case closed. My job is not to convince you, but to make sure others don't buy into more of this paradox fantasy.Todd

No, the paradox is not at all "resolved". I honestly did my best to just stay out of this whole conversation, but there is no other way around it. I read through all your posts, none of them offer any resolution to this issue. I pray people reading this aren't taken in. I feel like I'm taking crazy pills.

First of all, energy conservation when the drive is on a ship that is accelerating is a red herring. It's been stated and shown so many times that I'm not going to bother to link it, but a COE paradox exists if the drive is just attached to a wheel and spun at a great enough velocity. No tangential acceleration. The energy source need not be attached to the wheel itself, so your expression for Eout doesn't hold. Even if what you posted previously worked, which it doesn't, you wouldn't have resolved the COE issue.

Come back to the Newtonian version you posted here. This time, instead of assuming COE by equating Ein and Eout, let Ein=Pin*t. Now let k=F/Pin and solve for v. You can do this the hard way with integral of F/m(t), where m(t)=mo-Pin*t/c2 or do it the easy way by realizing you underestimate v (and consequently Eout) if you just set m(t)=mo (v=(Pin*k*t)/mo). Thus this simplification sets a lower Eout then in actuality,

Go through that procedure as I just did with a k greater than 1/c. See if Ein<Eout for some v<c.

Quote

Paradox resolved, case closed. My job is not to convince you, but to make sure others don't buy into more of this paradox fantasy.

Out of all the things involving the EMdrive, the COE paradox is one of the least fantasy of them all.

Thank you! I was getting tired of being the sole defender of mainstream physics. Your mathematical suggestions are cogent and valid, and put the argument to bed in favour of known physics.

A predominantly qualitative argument easily demonstrates the incorrectness of WarpTech's approach. According to him, the error in my rather elementary Newtonian analysis arises from a lack of consideration of the mass loss of the battery. He asserts this despite the fact that the systems under consideration here are expected to have a mass on order tens of kilograms. Well, let's run the numbers.

Let's take a ridiculously powerful battery and run it for a long time, in the context of an on-board EmDrive power source. Say 1 MW for 1 hour. This produces a total output energy of 3.6*109 Joules. WarpTech's correction demands we express this as an equivalent mass, which we do by dividing by c2, a huge number of magnitude roughly 1017. What we get is an equivalent mass of 3.6*10-8 Kg. When we compare this smidgeon with a typical system mass of probably north of a metric ton, we can see that it is so far down in the noise as to be completely insignificant. It cannot possibly make any substantive difference to the power breakeven velocity = 1/k.

The attached instrument display insets are return loss measurements, S11 of about 23.5dB or 1.14:1 VSWR (on the right) and should not be confused as S21, ampliture response in the frequency domain. There are also no time domain measurements (phase) in the passband. No idea if it is linear. Also, would liked to have seen passband Group Delay measurements in nSecs; Bessel usually has fairly flat GD, is it a true bessel? Is there little ringing or overshoot in pulsed measurements ala Gaussian?

So many questions, so few answers...suffice it to saw there is only partial disclosure by all parties here.

The irony in WarpTech's incorrect theory claiming that over-unity is "a fantasy" is that, as pointed out by @wallofwolfstreet, it tends to make it easier to achieve over-unity - by lowering the critical velocity below the Newtonian value!

The irony in WarpTech's incorrect theory claiming that over-unity is "a fantasy" is that, as pointed out by @wallofwolfstreet, it tends to make it easier to achieve over-unity - by lowering the critical velocity below the Newtonian value!

WarpTech's theory in its relativistic version, which should be deemed as the correct one, is fatally flawed. It predicts an imaginary break-even (Eout=Ein) velocity for the limiting case Ein=0.

The irony in WarpTech's incorrect theory claiming that over-unity is "a fantasy" is that, as pointed out by @wallofwolfstreet, it tends to make it easier to achieve over-unity - by lowering the critical velocity below the Newtonian value!

I'd have to work it out exactly, (and I probably won't have time) but the centrifugal "force" should distort the mode such as to limit the accelerating force available as a function of angular velocity. (Due to the taper of the cavity) So there is a very good chance that over-unity is just fantasy.

The irony in WarpTech's incorrect theory claiming that over-unity is "a fantasy" is that, as pointed out by @wallofwolfstreet, it tends to make it easier to achieve over-unity - by lowering the critical velocity below the Newtonian value!

WarpTech's theory in its relativistic version, which should be deemed as the correct one, is fatally flawed. It predicts an imaginary break-even (Eout=Ein) velocity for the limiting case Ein=0.

This is because I attempted to satisfy the condition that Eout=Ein. Since this is an impossible condition, you get an impossible answer.

I'm back and I'm glad you all didn't verbally slash and gash your way to figuring out the Q of a frustum. Or the way the EMDrive does what it does while violating CoE CoM or not. The EMDrive is going to do what it wants.

We're close to where we were hundreds of pages ago. Nobody knows for sure, that's it. It's simple as that. You all need data plain and simple, heck I need data.

The EMDrive will do what physics says it can do and that is the ultimate calculator of forces and formulas. This is why I swallowed my pride and did a gofundme. I WILL build one of these babies and test it inside out and upside down using the ultimate calculator, mother nature, we all pale to her breadth and depth of knowing what will happen.

I've tried to come up with a game plan of what ifs and feel free to add to it.

What if it just sits and hums? Regroup, recheck, re-evaluate, re-test, ask for help.

What if it thrusts the wrong way" Regroup, recheck, re-evaluate, re-test, ask for help.

What if the drive shoots off the fulcrum and measurements show it violates CoE and Newton and Maxwell are turning over in their graves? Regroup, recheck, re-evaluate, re-test, ask for help.

What if it kind of works with tiny itsy bitsy thrust? Regroup, recheck, re-evaluate, re-test, ask for help.

What if it really works and we get measured movement and thrust? Regroup, recheck, re-evaluate, re-test, ask for help.

I can regroup, I can recheck, I can re-test, but help has to come from here. I have little control over the quality of help or the cooperation of help. I need this cooperation, we need this. I'll be spending countless hours making sure we get what we need, all I'm asking is cooperation I can depend on to reach our goals. This is a cooperative hunt, not who can stand alone on the hill and pee the furthest.

Ok, off my soapbox, but this is part of the equation that needs to be met in figuring out the why to one of the strangest problems I've seen in all my decades in the field. I can't do this alone.

I'm back and I'm glad you all didn't verbally slash and gash your way to figuring out the Q of a frustum. Or the way the EMDrive does what it does while violating CoE CoM or not. The EMDrive is going to do what it wants. ...

The verbal slashing and gashing is an unfortunate outcome of Internet Forum discussions where people (actually men: I don't see women doing this here ) interface using monickers and not face to face. It would not happen if people were to have the same conversation in a cafe.

However, something good came out of this discussion: it is apparent that there are no IEEE or international organization standards of how to measure and report loaded Q's. Nobody has yet brought up any such standard.

Authors have reported Q's sometimes without clearly reporting how they determined such Q's. So, it is quite probable that people are using different ways to measure and report Q values, and this is a source of miscommunication. It would be like people with different languages using the same word to describe something but with different meanings.

The irony in WarpTech's incorrect theory claiming that over-unity is "a fantasy" is that, as pointed out by @wallofwolfstreet, it tends to make it easier to achieve over-unity - by lowering the critical velocity below the Newtonian value!

WarpTech's theory in its relativistic version, which should be deemed as the correct one, is fatally flawed. It predicts an imaginary break-even (Eout=Ein) velocity for the limiting case Ein=0.

The irony in WarpTech's incorrect theory claiming that over-unity is "a fantasy" is that, as pointed out by @wallofwolfstreet, it tends to make it easier to achieve over-unity - by lowering the critical velocity below the Newtonian value!

I'd have to work it out exactly, (and I probably won't have time) but the centrifugal "force" should distort the mode such as to limit the accelerating force available as a function of angular velocity. (Due to the taper of the cavity) So there is a very good chance that over-unity is just fantasy.

That muddies the waters, in that a rotary implementation is not the only implementation. A linear reciprocating engine may also be built and achieve a similar objective of producing over-unity energy. Perhaps "mode distortion" is also present for the linear case, but that's above my pay grade.

I used @wallofwolfstreet's approximation and ratio'd it with the exact solution (which is pretty horrific). We are substantially correct in saying that @WarpTech's maths results in a lower energy breakeven velocity, which is 2/k for pure Newtonian. @WarpTech is therefore incorrect in saying that there's no break-even: in actual fact he predicts that it's easier.

...Out of all the things involving the EMdrive, the COE paradox is one of the least fantasy of them all.

...Let's take a ridiculously powerful battery and run it for a long time, in the context of an on-board EmDrive power source. Say 1 MW for 1 hour. This produces a total output energy of 3.6*109 Joules. WarpTech's correction demands we express this as an equivalent mass, which we do by dividing by c2, a huge number of magnitude roughly 1017. What we get is an equivalent mass of 3.6*10-8 Kg. When we compare this smidgeon with a typical system mass of probably north of a metric ton, we can see that it is so far down in the noise as to be completely insignificant. It cannot possibly make any substantive difference to the power breakeven velocity = 1/k.

I rest my case... Force goes to zero at a limiting velocity, even in the Newtonian case.Todd

I'm back and I'm glad you all didn't verbally slash and gash your way to figuring out the Q of a frustum. Or the way the EMDrive does what it does while violating CoE CoM or not. The EMDrive is going to do what it wants. ...

The verbal slashing and gashing is an unfortunate outcome of Internet Forum discussions where people (actually men: I don't see women doing this here ) interface using monickers and not face to face. It would not happen if people were to have the same conversation in a cafe.

However, something good came out of this discussion: it is apparent that there are no IEEE or international organization standards of how to measure and report loaded Q's. Nobody has yet brought up any such standard.

Authors have reported Q's sometimes without clearly reporting how they determined such Q's. So, it is quite probable that people are using different ways to measure and report Q values, and this is a source of miscommunication. It would be like people with different languages using the same word to describe something but with different meanings.

Q is such a tough one and at least it came out there is no real standard. This is why I didn't post my Q, it's so open for debate and in the real world testing this device, it is, what it will be. (hopefully >2)Shell

...Out of all the things involving the EMdrive, the COE paradox is one of the least fantasy of them all.

...Let's take a ridiculously powerful battery and run it for a long time, in the context of an on-board EmDrive power source. Say 1 MW for 1 hour. This produces a total output energy of 3.6*109 Joules. WarpTech's correction demands we express this as an equivalent mass, which we do by dividing by c2, a huge number of magnitude roughly 1017. What we get is an equivalent mass of 3.6*10-8 Kg. When we compare this smidgeon with a typical system mass of probably north of a metric ton, we can see that it is so far down in the noise as to be completely insignificant. It cannot possibly make any substantive difference to the power breakeven velocity = 1/k.

I rest my case... Force goes to zero at a limiting velocity, even in the Newtonian case.Todd

I would advise against resting it. You have made the same mistake as you did some time ago. You cannot write "v = a t" for this nonlinear dynamic. You have to integrate.

Nevertheless, I'll flog through a full treatment because, despite the logical error, it's an interesting observation. More to follow, I hope.

ETA: You are implicitly assuming that 'k' is variable. If that's the case, then it's a function of velocity, and we're back to a preferred rest frame. If you want to go that route, simply write F = Pin/v by pretending that the EmDrive "knows" its velocity somehow. Now you have Ein=Eout and Pin=Pout at all times, and all energy conservation considerations are satisfied.

Unfortunately, IMHO spacetime is not a road and EmDrive is not a tyre riding on it.

I'm back and I'm glad you all didn't verbally slash and gash your way to figuring out the Q of a frustum. Or the way the EMDrive does what it does while violating CoE CoM or not. The EMDrive is going to do what it wants. ...

The verbal slashing and gashing is an unfortunate outcome of Internet Forum discussions where people (actually men: I don't see women doing this here ) interface using monickers and not face to face. It would not happen if people were to have the same conversation in a cafe.

However, something good came out of this discussion: it is apparent that there are no IEEE or international organization standards of how to measure and report loaded Q's. Nobody has yet brought up any such standard.

Authors have reported Q's sometimes without clearly reporting how they determined such Q's. So, it is quite probable that people are using different ways to measure and report Q values, and this is a source of miscommunication. It would be like people with different languages using the same word to describe something but with different meanings.

Q is such a tough one and at least it came out there is no real standard. This is why I didn't post my Q, it's so open for debate and in the real world testing this device, it is, what it will be. (hopefully >2)Shell

Shell, you know shat "Specsmanship" is, right? Think of Q that way...people can define it differently to show as high a number as they want. "The bigger the Q, the better it is" type attitude. As Doc said, who knows if Q is even a relavent number...it contains no measurement, only a ratio. It is relative to common industrial standards, unfortunately not across all disciplines.

...Out of all the things involving the EMdrive, the COE paradox is one of the least fantasy of them all.

...Let's take a ridiculously powerful battery and run it for a long time, in the context of an on-board EmDrive power source. Say 1 MW for 1 hour. This produces a total output energy of 3.6*109 Joules. WarpTech's correction demands we express this as an equivalent mass, which we do by dividing by c2, a huge number of magnitude roughly 1017. What we get is an equivalent mass of 3.6*10-8 Kg. When we compare this smidgeon with a typical system mass of probably north of a metric ton, we can see that it is so far down in the noise as to be completely insignificant. It cannot possibly make any substantive difference to the power breakeven velocity = 1/k.

I rest my case... Force goes to zero at a limiting velocity, even in the Newtonian case.Todd

I would advise against resting it. You have made the same mistake as you did some time ago. You cannot write "v = a t" for this nonlinear dynamic.

Nevertheless, I'll flog through a full treatment because, despite the logical error, it's an interesting observation. More to follow, I hope.

ETA: You are implicitly assuming that 'k' is variable. If that's the case, then it's a function of velocity, and we're back to a preferred rest frame. If you want to go that route, simply write F = Pin/v by pretending that the EmDrive "knows" its velocity somehow. Now you have Ein=Eout and Pin=Pout at all times, and all energy conservation considerations are satisfied.

Unfortunately, IMHO spacetime is not a road and EmDrive is not a tyre riding on it.

Ah, but you are forgetting that the vehicle's battery does know. The vehicle started at rest with a total rest energy of m0*c^2, and it ended at it's final velocity, totally depleted of battery power with a rest energy of (m0*c^2 - Ein). It has less rest-energy. So it knows it has been spent. Besides, this is Newtonian mechanics, relativity does not apply. Newton used a preferred rest frame. I can add a few factors of gamma and a Lorentz transformation if you want to make that argument, but I'd prefer to put this damn thing to bed.Todd